Minimum requirements for Debian are: 486, 48 MB RAM, ~250 MB HDD (not including swap space). But that means: no GUI, no eye candy, and a good knowledge of what you're doing.

For beginners it's probably better to start with OpenSuSE/Fedora/Ubuntu/Mint, and work you way down. But for those to feel good you'll need (guesstimating here) a P3 ~1GHz, 512 MB RAM, and about 1 GB HDD space.

If you've got a reasonable system already you could give VirtualBox or VMware a try.